Alternating Current Class 12 Physics Chapter 7 Test 2026-27

Alternating Current Class 12 Physics Chapter 7 Test 2026–27

A complete, original chapter test for CBSE Class 12 Physics covering RMS values, reactance, impedance, series LCR circuits, resonance, power factor, AC generator and transformer.

Class 12 PhysicsChapter 7CBSE 2026–2750 MarksAnswers Included

What this test is: An original Learn Revise Hub Alternating Current Class 12 Physics chapter test designed for focused board preparation. It is not an official CBSE paper. The current CBSE 2026–27 Physics SQP remains a 70-mark, 3-hour paper with five sections; this page adapts the assessment style into a 50-mark chapter-only practice test so students can test Chapter 7 independently.

Official CBSE Physics Curriculum 2026–27 · Official Class XII 2026–27 SQP & Marking Scheme

Recommended time: 90 minutes   |   Total: 50 marks
Best method: Attempt the full test first. Do not open the answer key while solving. Use the worked solutions only after completing your attempt.

1. Current CBSE 2026–27 Syllabus Boundary

This test follows the current Chapter 7 scope: alternating current, peak and RMS values, reactance, impedance, series LCR circuit at the phasor level, resonance, power in AC circuits, power factor, wattless current, AC generator and transformer. The official curriculum groups Chapters 6 and 7 within Unit IV, which carries 18 marks jointly; CBSE does not prescribe a separate fixed mark allocation for Chapter 7 alone. Topics outside the current core boundary are not treated as required test content here.

Important boundary note: Some older and competitor resources include topics such as Q-factor/sharpness of resonance or broader competitive-exam extensions. They may be useful elsewhere, but they are not used as required Chapter 7 content in this test unless a student is intentionally studying beyond the CBSE core.

2. Test Pattern & Mark Distribution

Section	Coverage	Questions	Marks
A	MCQs + Assertion–Reason	10 MCQs + 4 A–R	14
B	Short-answer concepts	6 × 2 marks	12
C	Numericals + reasoning	5 × 3 marks	15
D	Case-based application	1 case × 4	4
E	Integrated long numerical	1 × 5 marks	5
Total			50

3. Section A — MCQs and Assertion–Reason (14 marks)

Questions 1–10: Choose the correct option. Questions 11–14: use the standard Assertion–Reason code.

Assertion–Reason code: (A) Both A and R are true, and R is the correct explanation of A. (B) Both A and R are true, but R is not the correct explanation of A. (C) A is true, but R is false. (D) Both A and R are false.

Q1. 1 mark A sinusoidal AC current has peak value 6 A. Its RMS value is:

A. 3 A

B. 6/√2 A

C. 6√2 A

D. 12 A

Q2. 1 mark The inductive reactance of an ideal inductor is:

A. 1/(2πfL)

B. 2πfL

C. 2πL/f

D. f/(2πL)

Q3. 1 mark When the frequency of an AC source increases, the capacitive reactance:

A. increases

B. decreases

C. remains constant

D. becomes zero at every frequency

Q4. 1 mark In a pure capacitive circuit, current:

A. lags voltage by 90°

B. leads voltage by 90°

C. is in phase with voltage

D. is always zero

Q5. 1 mark The impedance of a series LCR circuit at resonance is:

A. X_L + X_C

B. R

C. zero

D. √(R² + X_L²)

Q6. 1 mark At series resonance, the power factor is:

A. 0

B. 1

C. 1/2

D. dependent only on frequency

Q7. 1 mark If the number of turns in the secondary of an ideal transformer is twice the number in the primary, then:

A. V_s = V_p/2

B. V_s = 2V_p

C. I_s = 2I_p

D. frequency doubles

Q8. 1 mark The peak EMF of an ideal AC generator is proportional to:

A. 1/(NBAω)

B. NBAω

C. N/(BAω)

D. B/(NAω)

Q9. 1 mark The SI unit of impedance is:

A. henry

B. farad

C. ohm

D. watt

Q10. 1 mark In an ideal purely reactive circuit, the average power over a complete cycle is:

A. maximum

B. zero

C. equal to V_rmsI_rms

D. always negative

Q11. 1 mark Assertion (A): In a series LCR circuit at resonance, the current is maximum for a fixed RMS source voltage. Reason (R): At resonance, X_L = X_C, so the impedance becomes R, its minimum value for the series circuit.

Q12. 1 mark Assertion (A): Increasing frequency increases capacitive reactance. Reason (R): X_C = 1/(2πfC).

Q13. 1 mark Assertion (A): An ideal transformer changes the voltage magnitude but does not change the frequency of an AC supply. Reason (R): The turns ratio changes the frequency between primary and secondary.

Q14. 1 mark Assertion (A): An ideal pure inductor can have non-zero current but zero average power consumption. Reason (R): Current and voltage differ in phase by 90° in an ideal pure inductor.

4. Section B — Short Answer Questions (12 marks)

Q15. 2 marks A sinusoidal voltage is v = 200 sin(100πt) V. Find (i) its peak voltage and (ii) its frequency.

Q16. 2 marks State the phase relationship between voltage and current for (i) a pure resistor and (ii) a pure capacitor.

Q17. 2 marks A series LCR circuit is operating below its resonant frequency. State whether its net behaviour is inductive or capacitive and whether current leads or lags the source voltage.

Q18. 2 marks Why does a transformer not normally operate on a steady DC supply? Give the physical reason.

Q19. 2 marks Distinguish between peak value and RMS value of a sinusoidal AC voltage. Write their relation.

Q20. 2 marks Define power factor in an AC circuit. For a series LCR circuit, write its expression in terms of R and impedance Z.

5. Section C — Numericals and Reasoning (15 marks)

Q21. 3 marks An AC source has V_rms = 230 V and frequency 50 Hz. Find its peak voltage and angular frequency.

Q22. 3 marks A coil of inductance 0.20 H is connected to a 50 Hz AC source. Calculate its inductive reactance. What happens to X_L if the frequency is doubled?

Q23. 3 marks A capacitor of capacitance 100 μF is connected to a 50 Hz AC source. Calculate its capacitive reactance. State what happens to X_C if the frequency is doubled.

Q24. 3 marks A series LCR circuit has R = 20 Ω, X_L = 30 Ω and X_C = 10 Ω. Calculate (i) impedance and (ii) power factor. State whether the circuit is inductive or capacitive.

Q25. 3 marks A series LCR circuit has L = 0.20 H and C = 50 μF. Calculate its resonant frequency. Show the formula used and give the answer to an appropriate number of significant figures.

6. Section D — Case-Based Application (4 marks)

Case Study: Variable-Frequency LCR Circuit
A student connects a resistor, inductor and capacitor in series to an AC source whose frequency can be varied. At one frequency, the current becomes maximum. Measurements show that the source voltage and current are in phase at this frequency. When the frequency is increased further, the circuit becomes inductive.

Q26(a). 1 mark What condition identifies the frequency at which current is maximum?

Q26(b). 1 mark What is the phase angle at resonance?

Q26(c). 1 mark Above resonance, which is larger: X_L or X_C?

Q26(d). 1 mark If the resistance is increased while L, C and source voltage remain fixed, what happens to the maximum current at resonance?

7. Section E — Long Answer / Integrated Numerical (5 marks)

Q27. 5 marks A series LCR circuit is connected to an AC source of RMS voltage 200 V. Its resistance is 40 Ω, inductive reactance is 80 Ω and capacitive reactance is 50 Ω. (a) Calculate the impedance. (b) Calculate the RMS current. (c) Determine the power factor. (d) State whether the circuit is inductive or capacitive. (e) Calculate the average power consumed.

8. Answer Key

Q	Answer	Q	Answer
1	B	15	V₀ = 200 V; f = 50 Hz
2	B	16	R: in phase; C: current leads by 90°
3	B	17	Capacitive; current leads
4	B	18	Steady DC does not provide changing flux for normal transformer action
5	B	19	Vrms = V₀/√2
6	B	20	Power factor = cosφ = R/Z
7	B	21	V₀ ≈ 325 V; ω = 100π rad s⁻¹
8	B	22	XL ≈ 62.8 Ω; doubles
9	C	23	XC ≈ 31.8 Ω; halves
10	B	24	Z ≈ 28.3 Ω; PF ≈ 0.707; inductive
11	A	25	f₀ ≈ 50.3 Hz
12	D	26(a–d)	XL = XC; φ = 0; XL > XC; maximum current decreases
13	C	27	See worked solution below
14	A

9. Worked Solutions

Q15. Comparing v = V₀ sinωt with v = 200 sin(100πt), V₀ = 200 V and ω = 100π rad s⁻¹. Since ω = 2πf, f = 50 Hz.

Q16. In a pure resistor, voltage and current are in phase. In a pure capacitor, current leads voltage by 90° (π/2).

Q17. Below resonance, X_C > X_L, so the net reactance is capacitive and current leads the source voltage.

Q18. A transformer relies on mutual induction, which requires changing magnetic flux. A steady DC current produces essentially steady flux after the switching transient, so it cannot sustain transformer action and can cause excessive primary current/heating.

Q19. Peak value V₀ is the maximum instantaneous value of a sinusoidal voltage. RMS value is its effective heating-equivalent value. For a sinusoidal AC voltage, V_rms = V₀/√2.

Q20. Power factor is the cosine of the phase angle between voltage and current: PF = cosφ. For a series LCR circuit, cosφ = R/Z.

Q21. V₀ = √2V_rms = √2 × 230 ≈ 325 V. Also, ω = 2πf = 2π × 50 = 100π rad s⁻¹.

Q22. X_L = 2πfL = 2π × 50 × 0.20 ≈ 62.8 Ω. Since X_L ∝ f, doubling frequency doubles X_L to about 125.7 Ω.

Q23. X_C = 1/(2πfC) = 1/[2π × 50 × 100×10⁻⁶] ≈ 31.8 Ω. Since X_C ∝ 1/f, doubling frequency halves it to about 15.9 Ω.

Q24. Net reactance = X_L − X_C = 20 Ω. Z = √(R² + (X_L − X_C)²) = √(20² + 20²) ≈ 28.3 Ω. PF = R/Z ≈ 20/28.3 ≈ 0.707. Since X_L > X_C, the circuit is inductive.

Q25. f₀ = 1/(2π√LC) = 1/[2π√(0.20 × 50×10⁻⁶)] ≈ 50.3 Hz.

Q26. (a) Maximum current occurs at series resonance, where X_L = X_C. (b) At resonance φ = 0. (c) Above resonance, X_L > X_C. (d) At resonance Z = R, so I_max = V_rms/R; increasing R therefore decreases the maximum current.

Q27. Net reactance = 80 − 50 = 30 Ω. Z = √(40² + 30²) = 50 Ω. I_rms = 200/50 = 4 A. Power factor = 40/50 = 0.8. Since X_L > X_C, the circuit is inductive. Average power P = V_rmsI_rmscosφ = 200 × 4 × 0.8 = 640 W.

10. Self-Assessment

45–50: Strong chapter command.

35–44: Good preparation; rework the questions you missed.

25–34: Revisit RMS, R/L/C phase, reactance, LCR impedance, resonance and power factor.

Below 25: Revisit the Notes and Formula Sheet, then practise the MCQs and Numericals before retaking this test.

This is a practice-score interpretation, not an official CBSE grading scale.

11. Quick Answer Box — High-Intent Revision Questions

What is the RMS value of sinusoidal AC?

V_rms = V₀/√2 and I_rms = I₀/√2.

What is inductive reactance?

X_L = 2πfL; it increases directly with frequency.

What is capacitive reactance?

X_C = 1/(2πfC); it decreases as frequency increases.

What is the resonance condition in a series LCR circuit?

X_L = X_C, so Z = R, φ = 0 and current is maximum for a fixed source voltage.

What is power factor in an LCR circuit?

Power factor = cosφ = R/Z for a series LCR circuit.

What is the transformer turns-ratio relation?

For an ideal transformer, V_s/V_p = N_s/N_p and I_s/I_p = N_p/N_s.

12. High-Yield Final Checklist

✓ RMS and peak values are clearly distinguished.

✓ Pure R, L and C phase relationships are understood.

✓ X_L increases with frequency and X_C decreases.

✓ Series LCR impedance and phase angle can be calculated.

✓ Resonance condition and resonant frequency are clear.

✓ Power factor and average AC power are understood.

✓ Wattless current is not confused with zero current.

✓ Generator peak EMF relation e₀ = NBAω is known.

✓ Transformer voltage/current/turns relations are known.

13. Continue Chapter 7 Preparation

Chapter 7 Complete Notes Alternating Current Important Questions Alternating Current MCQs Alternating Current Numericals Case-Based Questions Assertion–Reason Practice Previous Year Questions (PYQs) Formula Sheet + Quick Revision Chapter 6 Notes Official CBSE Class XII SQP & Marking Scheme 2026–27

Source discipline: This chapter test is original Learn Revise Hub practice content. Official CBSE documents are the authority for current syllabus scope and assessment design. Competitor research was used only for search-intent and recurring practice-demand signals such as “Alternating Current Class 12”, RMS, reactance, impedance, LCR circuit, resonance, power factor, transformer and AC generator; no third-party question is presented as an official CBSE question.